Unclear about Nonstructural Restriction [WAS: Inferring Properties based on Types]

Hi, Evren!

Not about my rule encoding scheme this time, but a question about how to
correctly understand the "Nonstructural Restrictions" chapter, given in

  http://webont.org/owl/1.1/owl_specification.html#7

You wrote on Monday, October 01, 2007:

>Hi Michael,
>Your suggestion is a nice trick that almost works! In summary, you are 
>saying we can use the following set of OWL 1.1 axioms
>
>>     (R4) SubObjectPropertyOf( SubObjectPropertyChain(sibling 
>manman) brother)
>>
>>     (A1) SubClassOf( Man ObjectExistsSelf(manman) )
>>     (A2) SubClassOf( ObjectMinCardinality(1 manman owl:Thing) Man )
>>     (A3) ObjectPropertyDomain( manman Man )
>>     (A4) FunctionalObjectProperty( manman )
>>   
>to express the rule
>
>> (?x :hasSibling ?y) ^ :Male(?y) => (?x :hasBrother ?y)
>
>I think your set of axioms would do the trick but there is one 
>problem. 
>A1 together with A4 violates the non-structural restrictions on axioms 
>as explained in [1]. The same property cannot be both used in an 
>ObjectExistsSelf restriction and FunctionalObjectProperty 
>axiom (or any 
>other cardinality expression).

And in the following mail you wrote:

>When you read through that section you will actually see that those 
>nonstructural restrictions do not apply to the set of axioms you had in 
>the beginning :) It is ok to use the same property in (local or global) 
>reflexivity restrictions and cardinality restrictions at the same time. 
>The nonstructural restrictions only limit the usage of composite 
>properties (the only composite property in your set of axioms is 
>brother) so it wasn't a problem to begin with.

When I tried to verify this for my own understanding, I had difficulties to
understand the respective paragraph in this chapter. The first
"nonstructural restriction" says (at the end of the chapter):

    * Only simple object properties are allowed to occur 
      in [the axiom closure] Ax in

      * ObjectMinCardinality, ObjectMaxCardinality, ObjectExactCardinality, 
        and ObjectExistsSelf classes, 
        and

      * ObjectPropertyFunctional, InverseFunctionalObjectProperty, 
        ObjectPropertyIrreflexive, ObjectPropertyAsymetric, 
        and DisjointObjectProperty axioms.

Let's assume for this discussion that it is clear what a "simple" object
property is in this context, because this is not the important bit here. 

What I do not understand from this text is, what actually is allowed for
"simple" properties, and what actually is not allowed for non-simple
properties. Does the above paragraph say that simple properties can occur in
/all/ of the above axioms together (all axiom from both items '*')? Or just
in one of the first item and one of the second item? And for non-simple
properties: Aren't they allowed to occur in /any/ of the above axioms, or
are they only allowed in e.g. a 'ObjectMinCardinality' (first item), but
then not also in a 'AsymmetricObjectProperty' (second item)? And if a
non-simple property is allowed to occur in an 'ObjectExistsSelf' restriction
(first item), is it then also allowed to occur in another of the
restrictions of the first item, e.g. in an 'ObjectMinCardinality'
restriction? 

Ok, a lot of confusing questions, but this just results from me being
confused by this paragraph. :) I hope you see my problem. From what you
wrote above, I belive that you have more background knowledge about how
these nonstructural restrictions are meant. But for me, who only has this
single excerpt from the OWL-1.1 draft, it is hard to see what the correct
intention is. 

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: Michael.Schneider@fzi.de
Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555

FZI Forschungszentrum Informatik an der Universität Karlsruhe
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Received on Friday, 5 October 2007 11:04:46 UTC